CBSE Class 9 Mathematics Sample Paper SA1 2014 (2).pdf

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Summative Assessment-I Topper Sample Paper - 10 MATHEMATICS CLASS IX

Time: 3 to 3

1 hours 2

Maximum Marks: 80

GENERAL INSTRUCTIONS: 1. All questions are compulsory. 2.

The question paper is divided into four sections

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Section A: 8 questions (1 mark each) Section B: 6 questions (2 marks each) Section C: 10 questions (3 marks each)

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Section D: 10 questions (4 marks each) 3.

There is no overall choice. However, internal choice has been provided in 1 question of two marks, 3 questions of three marks and 2 questions of four marks each.

4.

Use of calculators is not allowed.

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SECTION – A

Q1.Which of the following is an irrational number? 2

(A) ( 5)

(B) ( 5 − 1) + (1 − 5) (C) (D)

5 5 25

Q2.Evaluate: 53 - 23 - 33 (A) 60 (B) 90 (C) 120 (D) 90




Q.3


An exterior angle of a triangle is 80° and two interior opposite angles are equal. Measure of each of these angle is:

(A) 120° (B) 40° (C) 100° (D) 60° Q4. The sides of a scalene triangle are in the ratio 3:5:7. If the perimeter of the triangle is 60 cm , then its area is : (A) 40 sq cm (B) 60√3 sq cm (C) 160√3 sq cm (D) 480√19 sq cm

Q.5

In figure -1, value of x is:

(A) 20°

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(B) 40°

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Heron’s formula is: (A) ∆ =

s(s + a)(s + b)(s + c

(B) ∆ =

(s − a)(s − b)(s − c)

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(C) 30°

(D) 50°

(C) ∆ = s(s − a)(s − b)(s − c) , s = a + b + c (D) ∆ = s(s − a)(s − b)(s − c) , 2 s = a + b + c Q.7

Q.8

Zero of the polynomial p (x) where p (x) = ax, a ≠ 0 is : (A) 1

(B) a

(C) 0

If p (x) =2 +

x3 x +x2 then p (-1) is : 2 3


(D)

1 a



(A)

15 6

(B)


17 6

(C)

1 6

(D)

13 6

SECTION –B

p where p and q are integers and q ≠ o. q

Q.9

Express 2. 9.3 in the form of

Q.10

1  If x =3 + 2 2 then find the value of  x −  . x 

Q.11

If 2x + 3y =8 and xy= 4 then find the value of 4x2+ 9y2.

3

OR If x2 +

Q.12

1 1  = 38, then find the value of  x −  . 2 x x 

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In figure -2, lines AB and CD intersect at O. If ∠AOD: ∠DOC= 4:5 then find ∠COB.

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Q.13

In figure -3 if PQ||RS then find ∠SOR

Q.14

In figure -4, ∆ABC and ∆ABD are equilateral triangles. Find coordinates of point C and D.





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SECTION - C Q.15

If

5+2 3 7+4 3

= a + b 3 then find the value of a and b.

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Simplify:

3 2

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3 −1

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−

6− 2

4 3

6+ 2

and y =

3+2 2

Q.16

If x =

Q.17

Find the value of x3+ y3 – 12xy + 64 when x+y = -4.

3 +1

3−2 2

then find the value of x + y.

OR If x= 2y + 6 then find the value of x3 -8y3 -36xy -216. Q.18

Factorize: 27 (x+y) 3 -8 (x-y) 3.

Q.19

Using suitable identity evaluate (998)3.

Q.20

A traffic island is a parallelogram with perimeter 84m. One of the sides is 24m and a diagonal is 30 m. Find the cost of surfacing at the rate of Rs 200 per sq m.

Q.21

In figure -5, if BE is bisector of ∠ABC and CE is bisector of ∠ACD, then show that 1 ∠BEC = ∠BAC. 2





Q.22

Show that in a right angled triangle, the hypotenuse is the longest

Q.23

In figure -6, if AB||CD, EF⊥CD and ∠GED = 126° then find ∠AGE, ∠GEF and ∠FGE.

Q.24

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In an isosceles triangle ABC with AB = AC, BD and CE are two medians. Prove that BD = CE.

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OR

In figure -7, if PS= PR, ∠TPS = ∠QPR then prove that PT = PQ.

SECTION – D Q.25

Prove that:





2x3+2y3+2z3 -6xyz = (x+y+z) [(x-y)2 (y-z)2+ (z-x)2] hence evaluate 2 (7)3 +2(9)3+2(13)3 -6(7) (9) (13). 3 2 Q.26 Factorize: 2y + y – 2y – 1.

OR If x+ Q.27

1 1 =5 then evaluate x6 + 6 . x x

In figure -8, If PQ ⊥ PS, PQ||SR, ∠SQR = 28° and ∠QRT = 65° then find the values of x and y.

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Q.28

Prove that sum of the angles of a hexagon is 720°.

Q.29

In a triangle ∆PQR, PR > PQ and PS is the bisector of ∠QPR. Prove that ∠PSQ.

Q.30

In figure – 9, two sides AB and BC and the median AM of ∆ABC are respectively equal to sides DE and EF and the median DN of ∠DEF. Prove that ∆ABC ≅ ∠DEF.

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∠PSR >

OR In figure – 10, PS is the bisector of ∠PQR and PT ⊥ QR. Show that ∠TPS =

1 (∠Q - ∠R) 2




Q.31 If a + b =

13 − 11 13 + 11

+

13 + 11 13 − 11


, find the value of a and b.

Q.32 Express the following in the form

p , where p and q are integers and q

q ≠ 0. (a) (b)

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0.001 2.3

Q.33 Factorise: x 4 − 13x2 + 36 .

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Q.34 Draw the quadrilateral formed by the points P(3, 0), Q(-4, 0), R(0, 5) and S(0, -7).

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